Related papers: Bridging Distance and Spectral Positional Encoding…

Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…

We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total…

Graph Neural Networks (GNNs) have received increasing attention for representation learning in various machine learning tasks. However, most existing GNNs applying neighborhood aggregation usually perform poorly on the graph with…

Recent advances in artificial intelligence have propelled the development of innovative computational materials modeling and design techniques. Generative deep learning models have been used for molecular representation, discovery, and…

Graph neural networks (GNNs) are important tools for transductive learning tasks, such as node classification in graphs, due to their expressive power in capturing complex interdependency between nodes. To enable graph neural network…

Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural networks (MPNNs) face well-documented theoretical and…

Graph Attention Network (GAT) is one of the most popular Graph Neural Network (GNN) architecture, which employs the attention mechanism to learn edge weights and has demonstrated promising performance in various applications. However, since…

We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…

Statistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations, such as the graph Laplacian or adjacency matrix. In this paper, we analyze the asymptotic…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…

This work introduces MiDi, a novel diffusion model for jointly generating molecular graphs and their corresponding 3D arrangement of atoms. Unlike existing methods that rely on predefined rules to determine molecular bonds based on the 3D…

Combining the message-passing paradigm with the global attention mechanism has emerged as an effective framework for learning over graphs. The message-passing paradigm and the global attention mechanism fundamentally generate node…

Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements…

Graph diffusion models achieve state-of-the-art performance in graph generation but suffer from quadratic complexity in the number of nodes -- and much of their capacity is wasted modeling the absence of edges in sparse graphs. Inspired by…

Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high-dimensionality of networks pose unique challenges to traditional dependency…

Learning the underlying distribution of molecular graphs and generating high-fidelity samples is a fundamental research problem in drug discovery and material science. However, accurately modeling distribution and rapidly generating novel…

Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems recently. However, poorly designed implicit GNN layers may have limited adaptability to learn graph metrics, experience…

Structural node embeddings, vectors capturing local connectivity information for each node in a graph, have many applications in data mining and machine learning, e.g., network alignment and node classification, clustering and anomaly…

A molecule's geometry, also known as conformation, is one of a molecule's most important properties, determining the reactions it participates in, the bonds it forms, and the interactions it has with other molecules. Conventional…